段路由的不相交路徑求解

 記錄下關於論文的理解，論文讀的一知半解的。
 在段路由中，段和段之間依然遵循最短路徑的原則。在不存在段路由的情況下，$forw(x\rightarrow y)$=SP(x,y)。在段路由存在的情況下，$forw(x_1\rightarrow ...\rightarrow x_k)=\cup_{i=1}^{k-1}forw(x_i\rightarrow x_{i+1})$。對於一條路徑$\vec p=forw(x_1\rightarrow ...\rightarrow x_k)，$在某些邊因爲故障失效後，段和段之間會重路由。 $f$是一條失效的邊，$f\in \mathscr{F}$。$forw(\vec p, f)=\cup_{i=1}^{k-1}forw(x_i\rightarrow x_{i+1},f)=\cup_{i=1}^{k-1} SP(x_i,x_{i+1},f)$。 $SP(x_i,x_{i+1},f)$表示重路由之後兩點的最短路徑。
 關於路徑是robustly disjoint的定義：路徑$\vec p_1$與路徑$\vec p_2$所有的邊不相交，在路徑某些邊失效後，重路由之後的路徑依然不相交。
  優化問題RDP(Min-max robustly disjoint sr-path problem)，找出這樣的路徑，且兩條路徑的最大時延最小。
 這個問題是NP難的。因爲[2]證明了求不相交路徑問題是NP-complete的。

關於SR場景的問題蒐集

• [16], SR的增量部署，MILP問題
• [18] ,K段問題K-MILP，使用CPLEX求解
• [19] In theory it was shown by [10] that for demand optimization with SR, selecting only one intermediate segment per demand is sufficient. One 2SR optimization took between
  80 and 110 seconds.
• The authors in [21] introduce an integer linear programming (ILP) model to heuristically evaluate the TE performance of SR-based packet networks. Three different ILP models are proposed, the ECMP model, SHP model, and SEGMR model. Because the computational complexity of the ILP model is high, some instances require too much time to be resolved. Thus, the authors propose a heuristic approach to determine the unique route between each pair of nodes that need to transmit information.
• [22]. The algorithm uses the criticality and congestion index of links to define the link weight. Then, the authors design the Bellman-Ford algorithm with a hop count restriction to solve the problem of minimum weight path.
• [23]使用粒子羣算法
  [1] Robustly Disjoint Paths with Segment Routing (https://pan.baidu.com/s/1RsfjvCfpQE0TUqZcoKVJpg 提取碼: 9xax)
  [2] Np-completeness of some edge-disjoint paths problems
  [3] Network Flows模型與python代碼求解，使用ortools
  [4] 網絡流（六）最小費用最大流問題
  [5] Find maximum number of edge disjoint paths between two vertices
  [6] Breadth First Search or BFS for a Graph
  [7] Models and Algorithms for Network Optimization
  with Segment Routing
  [8] IO競賽 圖論—網絡流
  [9] REPETITA: Repeatable Experiments for Performance Evaluation of Traffic-Engineering Algorithms
  [10] Optimized Network Traffic Engineering using Segment Routing
  [11] CG4SR: Near Optimal Traffic Engineering for Segment Routing with Column Generation
  [12] Expect the Unexpected: Sub-Second Optimization for Segment Routing
  [13] A Survey on Replica Server Placement Algorithms for Content Delivery Networks
  [14] Node-Constrained Traffic Engineering: Theory and Applications
  [15] Centrality-based Middlepoint Selection for Traffic Engineering with Segment Routing
  [16] Incremental Deployment of Segment Routing Intoan ISP Network: a Traffic Engineering Perspective
  [17] A Scalable and Error-Tolerant Solution for Traffic Matrix Assessment in Hybrid IP/SDN Networks
  [18] Traffic Engineering in Segment Routing Using MILP
  [19] Traffic Engineering Using Segment Routing and Considering Requirements of a Carrier IP Network
  [20] MPLS-based reduction of flow table entries in SDN switches supporting multipath transmission
  [21] Traffic engineering in segment routing networks
  [22] An efficient routing algorithm based on segment routing in software-defined networking
  [23] An Optimization Routing Algorithm Based on Segment Routing in Software-Defined Networks
  [24] Novel SDN architecture for smart MPLS Traffic Engineering-DiffServ Aware management
  [25] SDN-Based Data Center Networking With Collaboration of Multipath TCP and Segment Routing